Steyer, a major Democratic donor who also bankrolled last year's Proposition 39 campaign, said he thinks is it ridiculous that California is the only oil-producing state that does not levy such a fee on oil pumped from private land, which could generate billions of dollars a year for the state budget.

Proposals for an oil tax have stalled repeatedly amid pressure from oil companies, which are major donors to lawmakers' campaigns. But Steyer said he believes the current Legislature is more progressive and collaborative than in the past.

"I don't understand why the politics are hard here," he said in a telephone interview. "Who is going to stand up in the town square and say that we shouldn't have a tax on this?"

Tupper Hall, a spokesman for the Western States Petroleum Association, which represents oil companies, said Steyer is wrong to compare California with other states that have such a tax. He said oil companies generate a lot of revenue through other fees, including $500 million a year in state royalties and billions of dollars annually in royalties paid to private landowners for oil extracted on their property.

Hall said an extraction tax would mean more imported oil, decreased investment in the state's oil infrastructure and job losses.

"After understanding the implications of raising taxes on energy production, Californians have rejected all of those proposals and they will reject this one," Hall said.

State Sen. Noreen Evans, D-Santa Rosa, already has pending legislation that would impose a 9.5 percent per-barrel tax on oil, but it stalled in a legislative committee this year.

Her spokeswoman, Teala Schaff, said Evans hopes to find more support for the bill in 2014. But she noted that the current makeup of the Legislature includes more moderate Democrats who are loathe to oppose the business community, which has opposed such efforts.

"We're giving away our natural resources for free to companies that make billions of dollars a day in profits," she said. "If the Legislature can't get it done, then hopefully the people will."

Steyer says he will seek to persuade lawmakers through public polling that he believes will show voters support increasing taxes on major oil producers, but it could be a hard sell in 2014, an election year. The hedge fund founder from San Francisco said he has "no idea" of Gov. Jerry Brown's position on such legislation but cannot imagine the governor opposing it.

"It's very hard for me to understand how the governor couldn't be in favor of this," Steyer said. "But having said this, he's never said to me 'Don't worry, I'm behind this,'" he said.

Brown's press office did not immediately respond to a call seeking comment.

The governor has been dogged at events lately by protesters who oppose his signing of a law that sets rules for the method of extracting oil and natural gas known as hydraulic fracturing, or fracking. Opponents had sought a ban or stringent regulations on the practice. But of eight bills introduced on the issue this year, only one was signed into law, and opponents say that one was watered-down.

Steyer had a high-profile win in 2012, when voters approved his Proposition 39 by a 60-40 margin. The initiative closed a provision in the tax code that had allowed multistate corporations to choose between two tax formulas, which had cost the state about $1 billion a year in lost tax revenue. His effort was supported by many California-based businesses.

Steyer spent about $27 million of his own money on that campaign. He said he has not set a budget for how much he is willing to spend on a public awareness campaign for the oil-extraction tax.